Blender models adding extra faces in Element 3d
Looks like you have quite a few complex ngons in your model. The OBJ exporter may be getting confused. Before exporting to OBJ, in edit mode, select all the faces (or at least the ones giving you trouble), and hit Ctrl+T, which is 'triangulate faces'. This will convert all your quads and ngons into triangles.

Once converted, ensure those strange edges have not reappeared (and fix them if they do), then export to OBJ once again.